Rewrite as a simplified fraction. ${2.6\overline{52} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2652.5252...\\ 10x &= 26.5252...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2626}$ ${x = \dfrac{2626}{990}} $ ${x = \dfrac{1313}{495}} \text{or} {2 \dfrac{323}{495}}$